Big Idea:
In this lesson, students are introduced to a vertical number line as an effective tool for rounding large numbers and build conceptual understanding.

I begin this lesson with a math fluency assessment. In my classroom, student take a math fluency assessment each week and graph their results. This fluency assessment comes from a book entitled MBSP: Monitoring Basic Skills Progress: Basic Math. You can see the book cover below and a sample page.

The Common Core State Standards specify that fourth graders should be fluent in adding and subtracting to 1,000,000. This fluency assessment has mixed computation, including multiplication and division so students continue to practice these skills. Students have 3 minutes to complete 25 mixed computation problems.

Teacher Background: If you are not familiar with vertical number lines and rounding, you can watch the video below. This video also does a nice job at showing how students will use vertical number lines in later grades with decimals as well.

I begin this lesson by having students practice finding the midpoint between to endpoints on a vertical number line. I draw a vertical number line on the board and label the endpoints 20 and 30. I ask students what number is in the middle of 20 and 30. This is easy for students and they know it's 25.

Next I draw a another vertical number line and label the endpoints 2,000 and 3,000. I ask my students what is in the middle of 20 hundreds and 30 hundreds. Students have an easy time responding 25 hundreds since I used the first number line of 20 and 30. They are able to see patterns and relationships between the two number lines. I do the same thing for 20 and 30 thousands pointing out the similarities between all three number lines.

Note: For the next part of the lesson, some students recite rounding chants/rules they've learned in prior grades. I tell my students that those rules aren't wrong, but we are going to look at rounding visually in order to see numbers on a number line.

Next, I ask students how many thousands are in the number 5,100. I label one end point of a vertical number line 5,000. I encourage students to tell me the next end point by asking how many one more thousand would be. I then label the other endpoint 6,000. Students share that 5,500 is the midpoint between these numbers. If students hare having a difficult time, I change the way I ask this question by using place value. I change the names of my end points by calling them 50 hundreds and 60 hundreds. This scaffold is important and helps reinforce flexibility with place value.

Next, I direct students to place 5,100 on the number line. I remind students that 5,100 is closer to 5,000 so 5,100 rounds to 5,000. I repeat this procedure with 5,800.

Next, I use the same procedure for rounding five and six digit numbers to the thousands place. I use endpoints 16,000 and 17,000. Students determine what the midpoint is and then practice rounding several numbers. I list various numbers between these two endpoint and ask students to share their thinking about rounding the number. For example, I ask students to round 16,990 to the nearest thousand. Students share their thinking and explain why he/she thinks the number should be placed at a specific spot on the number line.

I continue this procedure for other number. When most of my students are understanding, I give time for students to practice independently - rounding to thousands practice. This practice page is from www.engageny.com.

As students work, I circulate around the room to check for understanding and clear up misunderstandings. This is an important part of the lesson. Most of my students have not had prior experience rounding numbers with a number line. Some students need re-assurance and questioning to help guide their thinking through the practice.

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Resources

I end this lesson by correct the independent practice with students. After the corrections, I have student volunteers use the whiteboard wall and round various numbers. I call this "show what you know." This is another opportunity for students to practice math talk. It is also an opportunity for students who understand the concept and number line to verbalize to the class and other students about his or her thinking. This is extremely beneficial for all learners. Students who are struggling get to hear the information again, presented in a different way while students who are nearing mastery have an opportunity to solidify their thinking by teaching others.